Question

The equation of line line y = (b/ac)x. Does the midpoint of line segment BC, given by the coordinates (a, c) on a coordinate plane, lie on the line given?

a) No, because (b/ac) b does not equal ac.
b) No, because (b/ac) (ac) does not equal b.
c) Yes, because (b/ac) b=ac.
d) Yes, because (b/ac) (ac)=b.

Answer 1

The midpoint of line segment BC lies on the line given by the equation y = (b/ac)x.

Step-by-step explanation:

The equation of the line is y = (b/ac)x. To determine whether the midpoint of line segment BC, given by the coordinates (a, c), lies on the line, we substitute the values of a and c into the equation and check if the equation holds.

Substituting the values into the equation, we have: c = (b/ac)a. Simplifying, we get: c = ba/c. This equation holds true, so the midpoint of BC, (a, c), does lie on the given line equation.

Therefore, the correct answer is: d) Yes, because (b/ac)(ac) = b.